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arXiv:2206.10667 · Erkenntnis

On the Common Logical Structure of Classical and Quantum Mechanics

Andréa Oldofredi, Gabriele Carcassi, C. Aidala

Published Jul 30, 2022• 0 citations
arXivHTMLPDF
DOI
10.1007/s10670-022-00593-z

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Starting from logical structures of classical and quantum mechanics we reconstruct the logic of so-called no-signaling theories, where the correlations among subsystems of a composite system are restricted only by a simplest form of causality forbidding an instantaneous communication. Although such theories are, as it seems, irrelevant for the description of physical reality, they are helpful in understanding the relevance of quantum mechanics. The logical structure of each theory has an epistemological flavor, as it is based on analysis of possible results of experiments. In this note we emphasize that not only logical structures of classical, quantum and no-signaling theory may be treated on the same ground but it is also possible to give to all of them a common ontological basis by constructing a “phase space” in all cases. In non-classical cases the phase space is not a set, as in classical theory, but a more general object obtained by means of category theory, but conceptually it plays the same role as the phase space in classical physics.
Decoherentism, as being developed by many outstanding contemporary physicists, and elaborated in a systematic form by French physicist Roland Omnčs, eliminates eventually the long-lasting quantum-classical dualism in physics. It proves that in consequence of decoherence effect, the laws of quantum mechanics (with their probabilistic character) turn into the deterministic laws of classical physics; it describes therewith a real process through which the phenomenal world as given immediately to our sensory perception arises from quantum fundamentals; accordingly, classical determinism is a direct and controlled consequence of quantum mechanics.At the same time, decoherentism elaborated quantum logic (which is based on Griffiths' notion of consistent histories and corresponds to quantum mechanics) and proves that when decoherence acts, classical logic becomes a special kind of quantum logic. Since classical logic is essentially a learned version of common sense, the decoherentistic approach shows that the validity of common sense has its foundation in the rules of quantum mechanics. Thus, decoherentism eliminates the conflicts between quantum theory and common sense (in doing so, it proves that the famous paradoxes of Schrödinger's cat and the wave function reduction as well as the EPR paradox came from the mistake of having no account of decoherence effect).Nevertheless, decoherentism admits that the logic of common sense and as well as determinism itself have some probability of error which can be estimated in principle. These probabilities are most often extremely small and the corresponding errors have no practical consequence.Contrary to both classical and pre-decoherentistic quantum dynamics, decoherentism implies that the logical structure of quantum mechanics must select a definite direction of time, which necessarily coincides with the one occurring in thermodynamics; this means that the 2. law of thermodynamics (together with the irreversibility of time finds its basis in the decoherentistic interpretation of quantum mechanics.Hence it follows that decoherentism is truly a scientific revolution because the former principles (such as the principle of quantum-classical correspondence) turns in its frame into ordinary laws whic are derived from more fundamental principles.Considering the fact that classical determinism is a necessary presupposition for all scientific experiments, decoherentism's ability to derive determinism from newly interpreted quantum mechanics enables us to characterise it with the metaphor of "serpent gnawing his own tail." This means that quantum mechanics (in its decoherentistic interpretation) is able to explain even its own basic presuppositions; or, in other words, the results of the development of physical science turns back in order to explain its starting point. This important advancement makes physics structurally analogous to Adam Smith's economics (and to its metaphysical transcriptions in Hegel's Logic), to evolutionary biology and other sciences dealing with spontaneous order and self-organisation.
Quantum information and computation may serve as a source of useful axioms and ideas for the quantum logic/quantum structures project of characterizing and classifying types of physical theories, including quantum mechanics and classical mechanics. The axiomatic approach of quantum structures may help isolate what aspects of quantum mechanics are responsible for what aspects of its greater-than-classical information processing power, and whether more general physical theories may escape some common limitations of classical and quantum theories. Also, by by helping us understand how existing quantum algorithms work, quantum structures analyses may suggest new quantum protocols exploiting general features of quantum mechanics. I stress the importance, for these matters, of understanding open and closed-system dynamics, and the structure of composite systems in general frameworks for operational theories, such as effect algebras, convex sets, and related structures.